Abstract
The definition of basic rough sets [3] depends upon either a single equivalence relation defined on a universe or several equivalence relations defined over the universe, taken one each taken at a time. In the view of granular computing, classical rough set theory is based upon single granulation. Extending this notion, a rough set model based on multi-granulations (MGRS) was introduced in [5]. In this approach, approximations of sets were defined through multiple equivalence relations on the universe and their properties were investigated. Using hybridization of fuzzy set [13] with rough set the concept of rough fuzzy set was introduced by Dubois and Prade [1]. Recently, a Rough Fuzzy Set Model was introduced and studied by Wu and Kou [12], which is based on Multiple Granulation. Topological properties of rough sets introduced by Pawlak in terms of their types were recently studied by Tripathy and Mitra [10]. These were extended to the context of incomplete multi granulation by Tripathy and Raghavan [11]. In this paper we introduce incomplete multigranulation on rough fuzzy sets, study their basic properties and extend the topological properties in [11] to this context. Our findings are true for both complete and incomplete fuzzy rough set models based upon multi granulation.
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Tripathy, B.K., Nagaraju, M. (2012). Topological Properties of Incomplete Multigranulation Based on Rough Fuzzy Sets. In: Krishna, P.V., Babu, M.R., Ariwa, E. (eds) Global Trends in Information Systems and Software Applications. ObCom 2011. Communications in Computer and Information Science, vol 270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29216-3_11
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DOI: https://doi.org/10.1007/978-3-642-29216-3_11
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